Computational Aspects of the Mobius Transform
This addresses a bottleneck in applying Dempster-Shafer theory for uncertainty handling in expert systems, offering a practical improvement for researchers and practitioners in AI and decision-making.
The paper tackles the computational inefficiency of the Möbius transformation in Dempster-Shafer theory, which hinders its use in expert systems, by introducing 'fast Möbius transformations' that are the fastest algorithms for this computation, leading to a much faster algorithm for Dempster's rule of combination.
In this paper we associate with every (directed) graph G a transformation called the Mobius transformation of the graph G. The Mobius transformation of the graph (O) is of major significance for Dempster-Shafer theory of evidence. However, because it is computationally very heavy, the Mobius transformation together with Dempster's rule of combination is a major obstacle to the use of Dempster-Shafer theory for handling uncertainty in expert systems. The major contribution of this paper is the discovery of the 'fast Mobius transformations' of (O). These 'fast Mobius transformations' are the fastest algorithms for computing the Mobius transformation of (O). As an easy but useful application, we provide, via the commonality function, an algorithm for computing Dempster's rule of combination which is much faster than the usual one.